Stability and dynamics of a spectral graph model of brain oscillations

Abstract

We explore the stability and dynamic properties of a hierarchical, linearized, and analytic spectral graph model for neural oscillations that integrates the structural wiring of the brain. Previously, we have shown that this model can accurately capture the frequency spectra and the spatial patterns of the alpha and beta frequency bands obtained from magnetoencephalography recordings without regionally varying parameters. Here, we show that this macroscopic model based on long-range excitatory connections exhibits dynamic oscillations with a frequency in the alpha band even without any oscillations implemented at the mesoscopic level. We show that depending on the parameters, the model can exhibit combinations of damped oscillations, limit cycles, or unstable oscillations. We determined bounds on model parameters that ensure stability of the oscillations simulated by the model. Finally, we estimated time-varying model parameters to capture the temporal fluctuations in magnetoencephalography activity. We show that a dynamic spectral graph modeling framework with a parsimonious set of biophysically interpretable model parameters can thereby be employed to capture oscillatory fluctuations observed in electrophysiological data in various brain states and diseases.

Author Summary: One of the open questions in the field of neuroscience is to understand how dynamic brain functional activity arises with the static brain structural wiring as a constraint. Here, we explore the properties of an analytic model that can accurately capture such a relationship, where the brain functional activity is captured by magnetoencephalography. We demonstrate the temporal and spectral richness of this model and how it is controlled by a small set of biophysically interpretable parameters. Finally, we show that these parameters can accurately capture the temporal fluctuations in magnetoencephalography activity—outlining a tractable strategy to capture oscillatory fluctuations observed in electrophysiological data in various brain states and diseases.